Question

Ina quadrilateral $ABCD$, $AB=AD$ and $CB=CD$. Prove that :(i) $AC$ bisects angle $BAD$.(ii) $AC$ is perpendicular bisector of $BD$.

Answer 1

$In\Delta AOBand\Delta AOD$

$AB=AD\left(Given\right)$

$\angle BAD=\angle DAO\left(ACbisectsA\right)$

$AO=AO\left(Command\right)$

$\Delta AOB=\Delta AOD$

$DO=BO⟹equation1$

$\angle AOB=\angle AOD$

$\angle AOB+\angle AOD={90}^o\Rightarrow equation2$

$Fromequation1and2$

$ACisbisectorofBD.$